Question

Match List-I with List-II. 

List-I	Order of reaction
A	Zero order
B	First order
C	Second order
D	Third order

 

List-II	Unit of rate constant
I	mol⁻¹ L s⁻¹
II	mol⁻² L² s⁻¹
III	s⁻¹
IV	mol L⁻¹ s⁻¹

• A. A-IV, B-III, C-II, D-I
• B. A-IV, B-III, C-I, D-II
• C. A-IV, B-II, C-I, D-III
• D. A-I, B-II, C-III, D-IV

Hint:

Unit of rate constant depends on order: zero order \(=\text{mol L}^{-1}\text{s}^{-1}\), first order \(=\text{s}^{-1}\), second order \(=\text{L mol}^{-1}\text{s}^{-1}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Topic:
This question belongs to "Chemical Kinetics." It explores the units of the rate constant ($k$), which is a fundamental part of the rate law for a chemical reaction. The units of $k$ are not fixed; they change depending on the overall order of the reaction. This ensures that the overall "Rate" of the reaction always maintains consistent units of concentration divided by time ($mol \cdot L^{-1} \cdot s^{-1}$).
Step 2: Key Formulas and Approach:
The general formula for determining the units of the rate constant for a reaction of order $n$ is: \[ \text{Units of } k = (mol \cdot L^{-1})^{1-n} \cdot s^{-1} \] We can also write this as $M^{1-n} \cdot s^{-1}$ where $M$ is molarity. By substituting the values $n = 0, 1, 2, 3$, we find the corresponding units.
Step 3: Detailed Explanation:

A. Zero order (n=0): Substituting $n=0$: $(mol \cdot L^{-1})^{1-0} \cdot s^{-1} = mol \cdot L^{-1} \cdot s^{-1}$. Matches with IV.
B. First order (n=1): Substituting $n=1$: $(mol \cdot L^{-1})^{1-1} \cdot s^{-1} = (mol \cdot L^{-1})^0 \cdot s^{-1} = s^{-1}$. Matches with III.
C. Second order (n=2): Substituting $n=2$: $(mol \cdot L^{-1})^{1-2} \cdot s^{-1} = (mol \cdot L^{-1})^{-1} \cdot s^{-1} = L \cdot mol^{-1} \cdot s^{-1}$. Matches with I.
D. Third order (n=3): Substituting $n=3$: $(mol \cdot L^{-1})^{1-3} \cdot s^{-1} = (mol \cdot L^{-1})^{-2} \cdot s^{-1} = L^2 \cdot mol^{-2} \cdot s^{-1}$. Matches with II.
Step 4: Final Answer:
The correct matching sequence is A-IV, B-III, C-I, D-II, which is option (B).